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#19 by Susanna Cuyler at Wed Jul 10 21:24:07 EDT 2019
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#18 by Sean A. Irvine at Wed Jul 10 19:28:36 EDT 2019
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#17 by Sean A. Irvine at Wed Jul 10 19:28:29 EDT 2019
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| NAME
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Smallest prime p such that there is a prime q satisfyinqsatisfying (2*n + 1)*p^2 - (2*n-1)*q^2 = 2, or 0 if no such p exists.
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| STATUS
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approved
editing
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Discussion
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| Wed Jul 10
| 19:28
| Sean A. Irvine: Typo.
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#16 by Bruno Berselli at Tue May 21 02:34:48 EDT 2013
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#15 by Michael B. Porter at Mon May 20 21:03:11 EDT 2013
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#14 by Michael B. Porter at Mon May 20 21:02:58 EDT 2013
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#13 by Michael B. Porter at Mon May 20 21:02:06 EDT 2013
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| COMMENTS
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Primes p such that there is a prime q satisfying 5*p^2 - 3*q^2 = 2: 26839, 6391493137, 254008138207585425442608775189866722064414803728945619713,...2540081 3820758542 5442608775 1898667220 6441480372 8945619713, ...
Primes q such that there is a prime p satisfying 5*p^2 - 3*q^2 = 2: 34649, 8251382159, 3279230963597100734829167292288094425179733518120308284159,...32792309 6359710073 4829167292 2880944251 7973351812 0308284159, ...
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| LINKS
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Eric W. Weisstein, MathWorld: 's World of Mathematics, <a href="http://www.mathworld.wolfram.com/PellEquation.html">Pell Equation</a>
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| AUTHOR
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_Irina Gerasimova_,_Giovanni Resta_, May 1516 2013
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| EXTENSIONS
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a(2) from Giovanni Resta, May 15 2013
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#12 by Michael B. Porter at Mon May 20 00:24:00 EDT 2013
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| DATA
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3, 26839, 11, 239, 379, 0, 0, 2265645101581690578396614544820226664714826144430220423848365997375382090219581071702657444200847100414193674411846431
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| COMMENTS
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a(8) = 22656451 0158169057 8396614544 8202266647 1482614443 0220423848 3659973753 8209021958 1071702657 4442008471 0041419367 4411846431 - Giovanni Resta, May 16 2013
Conjecture: a(6) = a(7) = 0. Charles R Greathouse IV reports that a(6) must have thousands of digits. - Michael B. Porter, May 19 2013
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#11 by Michael B. Porter at Mon May 20 00:17:16 EDT 2013
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#10 by Irina Gerasimova at Sat May 18 10:11:21 EDT 2013
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Discussion
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| Mon May 20
| 00:17
| Michael B. Porter: I don't think we can put a(6)=a(7)=0 since we don't have a proof.
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